Question
How many divisors does the number 5040
have?Solution
First, find the prime factorization of 5040: 5040 ÷ 2 = 2520 2520 ÷ 2 = 1260 1260 ÷ 2 = 630 630 ÷ 2 = 315 315 ÷ 3 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 So, the prime factorization of 5040 is: 5040 = 2⁴ × 3² × 5 × 7. The formula for the number of divisors is: (Number of divisors) = (Exponent of 2 + 1)(Exponent of 3 + 1)(Exponent of 5 + 1)(Exponent of 7 + 1). Therefore, the number of divisors = (4 + 1)(2 + 1)(1 + 1)(1 + 1) = 5 × 3 × 2 × 2 = 60. Correct option: e
‘A’ can do a piece of work in 15 days. ‘B’ can do 60% of the same work in 20 days. If they work together for the entire time and get paid Rs.145...
- 40 women working 10 hours a day take 12 days to complete a project. How many women working for 7 hours a day are needed to complete twice the given project...
Bholu and Golu have teamed up to finish a task. On his own, Bholu can complete 5 units of work each day. Golu, when working solo, can finish the entire ...
A and B working together, can do a piece of work in 4(1/2) hours. B and C working together can do it in 3 hours. C and A working together can do it in 2...
P can complete a job in 30 days. Q alone can complete the same job in 20 days. P works for 18 days and then the remaining job is completed by Q. How man...
A and B can complete a work together in 18 days. If A alone can complete one-third of the work in ‘x’ days and remaining work is completed b...
P and Q can finish a job working together in 24 days. P completes two-thirds of the task in 'd' days, and Q finishes the rest in ...
Pipe A alone can fill 75% of a cistern in 18 minutes. When both Pipe A and Pipe B are opened together, they can fill the entire cistern in 33 minutes. H...
P’s 4 days work is equal to Q’s 5 days work. If P and Q together can complete the work in 25 days then how much time Q will take to complete 40% of ...
- 50% of the work done by Meena in 2 days is equal to 25% of the work done by Lata in 5 days. If Meena can complete the job alone in 10 days, then how long w...
